Ratio & proportion (Higher)
GCSE Maths (1MA1) · Higher · exam-style practice, examiner-report intelligence and the tools that drill it.
The topic on one screen
- Reverse percentages: the increase itself tells you what one percent is worth — £240 from a 20% rise means 1% = £12.
- Direct proportion: y = kx. Find k from the given pair FIRST, then answer the question.
- Inverse proportion: y = k/x (or k/x2 when stated) — same two-step routine: find k, then substitute.
- Ratios in context: introduce a multiplier (parts of size m), turn the ratio into algebra, solve for m.
- Combining ratios: scale them to share a common term before merging.
- Non-calculator arithmetic is part of the mark: 8.46 ÷ 0.15 style divisions open the paper — shift both numbers until the divisor is whole.
Where students actually lose marks
Proportion questions are marked on the constant: quoting y = kx with k evaluated earns the method even if the final substitution slips — skipping straight to a guessed answer earns nothing.
June 2023 Paper 1H mark scheme (Q13)
In multi-step ratio problems the scheme rewards a clear representation (parts as algebra) — answers with no visible structure gamble everything on the final number being right.
June 2023 Paper 1H mark scheme (Q18)
An incorrectly cancelled final fraction loses the mark even when the uncancelled value was correct — finish, then leave it alone.
June 2023 Paper 1H mark scheme (general guidance)
Try it — exam-style
The price of a laptop increases by 15%. This 15% increase adds £90 to the price. Work out the price of the laptop after the increase.
y is directly proportional to x, and y = 21 when x = 1.5. Work out the value of y when x = 5.
3 kg of apples and 2 kg of pears cost a total of 140p. The cost of 1 kg of apples : the cost of 1 kg of pears = 1 : 2. Work out the cost of 1 kg of pears.
y is inversely proportional to the square of x, and y = 4 when x = 3. Find y when x = 2.
Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.
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